Final answer:
The question involves applying the product property of logarithms to simplify the expression 1/3 [log(x) + log(x + 1)], resulting in 1/3 log(x(x + 1)).
Step-by-step explanation:
The question pertains to logarithmic properties and can be addressed using the product property of logarithms. In logarithmic form, the product property states that log(xy) = log(x) + log(y), which applies to any logarithmic base, be it log10 or ln (the natural logarithm). When simplifying the expression 1/3 [log(x) + log(x + 1)], you can combine the two logarithms into a single logarithm by using this property:
1/3 [log(x) + log(x + 1)] = 1/3 log(x(x + 1))
This is due to the fact that addition within a logarithm denotes a product of the arguments. Furthermore, when a logarithm is raised to an exponent, as in logn(x), the exponent can come out in front as a multiplier. This explains the coefficient of 1/3 in front of the logarithm in the original expression.